Harmonic mean - 8th grade (13y) - examples

1. Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
2. Ten cashiers
Ten cashiers are open at Tesco. Customers wait an average of 15 minutes. How many other cashiers have to open to reduce the waiting time by 4 minutes?
3. Flowerbed
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
4. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
5. Logic
A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together?
6. Tractors
Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?
7. Cyclist
Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
8. Car
Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?
9. Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
10. Workers
Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B?
11. Workers
Two workers fulfill a certain task when working together for 5 days, the first if he worked himself done work in 13 days. How many days will do whole job a second worker?
12. Garden
Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together?
13. Parquet floor
Three workers laid parquet floor for 2.301 hour. The first one would do this work alone 7 hours, the second in 6 hours. For how many hours would fulfill this work the third worker, if he worked alone?
During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe
15. Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
16. Tanker
An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty?
17. Three workers
Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 14 days, B together with C for 23 days, A together with C for 13 days. How long it would take to complete the task every one of them alone? How long it would.
18. Steamship
Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports?
19. Blueberries
Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter?
20. Electronics: Resistors in parallel
From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω

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